- Reef-building corals, in partnership with their algae symbionts, have been on Earth for at least 200 million years.
Mutualism is a symbiotic relationship in which both the host organism and the symbiont benefit. However, the coral and algae mutualistic relationship is a little more complicated than the definition because the effects on the symbiotic algae are less clear than the effects on the hosts.  The mutualistic relationship has clear benefits for the reef-building corals. However, the benefits for the photosynthetic dinoflagellates in the corals, Symbiodinium, are less clear. 
It is important to remember that the conditions for a healthy relationship between the coral and the algae have fairly strict boundaries as far as water temperature, ocean acidity, and amount of sunlight. Because the coral-algae mutualistic relationship is dependent on a variety of factors, it is difficult to define a clear benefit for the symbiotic algae. The relationship can be a "shifting continuum" that can "under specific conditions shift into parasitism."  As said previously, environment factors, such as increased temperature and dirty water, can strain the relationship between the coral and the algae. This strain can occasionally cause the costs of the relationship to outweigh the benefits.
Corals are from the phyla Cnidaria  Because corals have a large area to volume ratio, the algae on the corals are able to absorb a lot of light for photosynthesis, given ideal conditions. Over 700 species of coral have been found to be in symbiosis with dinoflagellate algae.
Subcellular arrangement of the coral-algae mutualistic relationship::
The contents of the algae cell are surrounded by the algae's plasma membrane and cell wall. Outside the cell wall is the symbiosome, which is a multiple-layer membrane complex that is derived from the host coral. The symbiosome is surrounded by the coral's endodermal cell and then the coral's plasma membrane. This multi-membrane structure means that the substances shared between the two organisms pass through multiple cell membranes.
The relationship between the coral and the algae is considered an autotroph-heterotroph mutualistic relationship. The algae produces its own food from sunlight and inorganic compounds, so it is an autotroph. The heterotrophic coral gets its food from the algae. The relationship between the coral and the algae is difficult to study because the mutual benefit occurs when the coral and the algae are together. The benefits of the relationship to each organism do not occur when the two are separated. The algae requires nutrients that are derived from the host coral and from the environment that surrounds the coral, and the coral gets the products produced by the photosynthetic autotrophic algae.
Benefits to Corals:
Through photosynthesis, the algal dinoflagellates produce 90% of the carbon that corals need for calcification. 
Some coral species use the carbon from the algae to produce mucus. This mucus is important in feeding and in protection from mechanical damage and pathogens. 
The dinoflagellate algae release glycerol, sugars, organic acids, and amino acids.  These substances are all "mobile compounds, which are compounds that are translocated to the animal tissues. 
Algae enhances the growth of the calcium carbonate coral skeleton, which gives the coral stability for its health as well as its physical architecture. 
When the algae leaves the coral because of damaging environment conditions, otherwise known as coral bleaching, the corals suffer from the lack of support from the algae. Impacts of bleaching include reduced growth and reproduction, increased susceptibility to disease and mechanical damage, and occasionally death of the coral. 
Benefits to Algae:
Corals help transport carbon dioxide from the surrounding seawater to the photosynthetic dinoflagellate algae. The algae needs the carbon dioxide in order to complete photosynthesis.  The coral has an enzyme that acidifies the boundary layer to convert carbon to carbon dioxide. This carbon dioxide diffuses into the host coral. It is trapped by conversion to bicarbonate and is then transported to the symbiosome of the algae. 
Corals provide the algae with a habitat.
It is important to remember that the benefits to each organism of the relationship are difficult to determine as the benefits only occur while the relationship is occurring.
- Sumich, James L. An Introduction to the Biology of Marine Life, Seventh Edition. WCB/McGraw Hill. 1999.
- Saffo, Mary Beth. "Mutualistic Symbioses." ELS (n.d.): n. pag. - ELS. 15 July 2014. Web. 20 February 2015.
- Yellowlees, David, V. Rees, and William Leggat. "Metabolic Interactions between Algal Symbionts and Invertebrate Hosts." Plant, Cell, and Environment 31.5 (2008): 679-94. Wiley Online Library. John Wiley and Sons, 27 February 2008. Web. 20 February 2015.
- Venn, A. A., J. E. Loram, and A. E. Douglas. "Photosynthetic Symbioses in Animals." Journal of Experimental Botany 59.5 (2007): 1069-080. Journal of Experimental Botany. Oxford Journals, 10 February 2008. Web. 20 February 2015.